Question 1 (5 points) A Company is aiming to produce and market a new model line

Question

Question 1 (5 points) A Company is aiming to produce and market a new model line of motor boats. The production manager, now is lacing or-buy decision regarding the outboard motor to be installed on each of these boats. Based on the total cost involved, the s needs to decide whether to produce the motors internally or have them purchased from a vendor. Student's ID Producing the motors internally would require a fixed investment of S4 million in new facilities as well as a marginal pr cost of $2,000 for each motor produced. If purchased from a vendor instead, the price would be $6,000 per motor. would like to know the quantity "Q" at which the total sost of producing.or.purchasing the.motors wosld be the same (a) Write the algebraic term that describes the total purchasing.costs-( point) (2 points) (c) Find the value of Q where purchasing costs is equal to production costs. (2 points) Student's ID A farmer has a 1000-acre farm on which carrots and tomatoes could be planted for the upcoming sesn He hes fertilizer and enough insecticides to cover at most 900 acres of carrots and 800 acres of ates While all the pl use the same fertilizer, the carrots' require different types of insecticide than the tomatioes Each scre olcure ertilized andone ton of the carrots' insecticide Similarly, each planted acre of tomates rqire g the tomatoes insecticide. Based on the ma be at least half the number of acres sthe allocakes for plonting curmrots Consider the especte ket demands, the farnner is keen on makingue ththe plnted of profit figures per ac Your model should include full definitions of the decision variables, Objective function and constri Variables: (2 points) Obiectivefunstion: (2 points) max-800 + 800 >1,600 Constraints (6 points)

Explanation / Answer

Please find below answer to question 1 :

Let,

Fixed ( investment ) cost = FC

Marginal production cost = MC per unit

Purchase price from vendor = P per unit

Relevant quantity = Q

PQ = FC + MC.Q

Or . PQ – MC.Q = FC

Or, Q x ( P – MC ) = FC

Or, Q = FC / ( P – MC )

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